Unable to Weight Paint in 3D viewport
You have 'Face selection masking' turned on in the 3D view header (2.79):



The selection masking options in 2.8 are found here:



This means that only faces that are selected in edit mode will be able to be painted on when weight painting. It's useful to use as a mask in case you want certain parts of the mesh to be excluded from weight painting.

Either disable this button or select all the faces that you want to weight paint in edit mode before returning to weight paint mode.